Fourier transform optical object analyzer

ABSTRACT

Fourier transform optical object analyzer comprising a plane support for an optical object to be analyzed, a mask formed with a slit registering with a line of the optical object and movable in a plane parallel to the object plane for line-by-line unmasking of the object and a grid including contiguous transparent and opaque zones bounded by curves in the form of equilateral hyperbolae. The mask is shifted step by step relatively to the optical object support and takes a plurality of discrete positions with regard to said object support. The grid is continuously shifted relatively to the mask for each position thereof and a photosensitive detector receives the light flux from the object which has passed through the slit and the grid. Means are provided for vibrating the grid relative to the object at a predetermined frequency, and for filtering the component of the output of the photosensitive detector at said frequency.

[451 Jan. 18, 1972 FOURIER TRANSFORM OPTICAL OBJECT ANALYZER [72]Inventor: Andr J. Girard, Chatillon, France [73] Assignee: OfficeNational DEtudes et de Recherches Aerospatiales, Chatillon-Sous-Bagneux,France [22] Filed: Sept. 28, 1970 [21] App]. No.: 76,027

[30] Foreign Application Priority Data Sept. 30, 1969 France ..6933343[52] U.S. Cl ..250/237, 350/162 SF [51] Int. Cl. ..H0lb 5/18 [58] Fieldof Search ..250/237; 350/162 SF [56] References Cited UNITED STATESPATENTS 3,090,281 5/1963 Marechal et a1 ..350/162 SF 3,305,692 2/1967Girard ..250/237 3,370,268 2/1968 Dobrin et al... ...350/162 SF3,497,287 2/1970 Lang ...350/l62 SF 3,511,571 5/1970 Ogle ..350/162 SFV/B PA 70/? 20 OTHER PUBLICATIONS Paris et al., A Method for Exceedingthe Cutoff Frequency of a Bandlimited Optical System, IBM TechnicalReport No. 02.281, Dec. 5, 1963.

Primary ExaminerRonald L. Wibert Assistant Examiner-Edward S. BauerAttorney-Abraham A. Saffitz ABSTRACT Fourier transform optical objectanalyzer comprising a plane support for an optical object to beanalyzed, a mask formed with a slit registering with a line of theoptical object and movable in a plane parallel to the object plane forline-by-line unmasking of the object and a grid including contiguoustransparent and opaque zones bounded by curves in the form ofequilateral hyperbolae. The mask is shifted step by step relatively tothe optical object support and takes a plurality of discrete positionswith regard to said object support. The grid is continuously shiftedrelatively to the mask for each position thereof and a photosensitivedetector receives the light flux from the object which has passedthrough the slit and the grid. Means are provided for vibrating the gridrelative to the object at a predetermined frequency, and for filteringthe component of the output of the photosensitive detector at saidfrequency.

4 Claims, 9 Drawing Figures PATENTEUJAMBIBYZ 3.638367 sum 1 0F 6INVENTOR:

Andre J. GIRARD PATENTEU JAN 1 8 I972 SHEET 3 0F 6 FlG.3

INVENTOR:

Andre J GIRARD TT E x By 42 RECORDER INVENTOR:

Andre J. GIRI XRD ATTO Y SHEET 5 [1F 6 T m/E152? 20 INVENTOR:

Andre J. GIBARD y SHEET 8 UP 6 INVENTOR:

Andre J. GIRA RD ZF'W FOURIER TRANSFORM OPTICAL OBJECT ANALYZER Thisinvention relates to improved Fourier transform optical objectanalyzers.

My U.S. Pat. No. 3,305,692 issued Feb. 21, 1967 and assigned to the sameassignee as the present application has disclosed Fourier transformplane object analyzers comprising means for defining a number of narrowstrips on the object, means for shifting past the object as many timesas there are strips therein a variable-transparency grid or lattice orthe like whose structure depends upon the kinetic form of the shiftingmovement and is such that as it moves the grid modulates the light fluxissuing from at least one straight strip of the object at a frequencydepending upon the relative position of the grid and object at thebeginning of the shift, and means for collecting on a radiation receiversequential signals forming components from which the Fourier transformsof the luminance or transparency functions of the object strips can bederived.

When the strips are perpendicular to the direction of shifting (in whichcase it will be said that the strips are disposed along the lines of theobject) and are sequentially isolated by means of a mask formed with aslit which unmasks the strips one by one, the process according to theinvention of my previous U.S. patent directly provides the Fouriertransforms of the luminance or transparency function of the objectstrips. in this case the analysis is said to be one-dimensional.

When the strips are parallel to the direction of shifting (in which caseit will be said that the strips are disposed in the direction of theobject columns) and are not isolated from one another by a slitted mask,each grid shift produces a component of the Fourier transform of theluminance or transparency function of each of the object strips, thecomponent for any strip depending upon the relative position of the gridand object in the direction perpendicular to the shift direction at thebeginning of each shifting movement. in this case the analysis is saidto be two-dimensional.

in the previous systems just outlined, the output signals have aconstant component at a time-dependent component representing, dependingupon whether the particular grid used is symmetrical or antisymmetrical,the even or odd part (or a component of such even or odd part) of theFourier transform of the luminance or transparency function.

It is an object of this invention to obviate the DC component of thesignal.

ONE-DIMENSIONAL ANALYSIS The mask slit registers with an object lineparallel to the xaxis and the grid is moved along the y-axis; thespatial frequency 0' of the grid along a straight line parallel to y isproportional to x. The grid transparency function is:

2y=l cos 2110 If B(x) or B( 0') (since 0- is proportional to x) is theluminance or transparency function of the object along the line inregistration with the mask slit, the light receiver output signal is:

tion, there is no need to know the odd part of the Fourier transform (inthe integral Fourier development of the lu minance or transparencyfunction the imaginary part thereof corresponds to the odd part of thetransform).

As already stated, it is an object of the invention to obviate theconstant term in the light receiver signal expressed byformula( l) bymaking the grid perform a vibratory movement around its instantaneousposition, the vibrating movement being independent of the actualmovement of the grid relatively to the object.

Let: y=y+a cos wt denote this vibratory movement. If y is substitutedfor y in 5 formula l we obtain:

+%f B(a) cos 21mg cos [2mm cos wtlda 1 W 1 B(a) sin 21mg sln [21mm coswtldo' 0 The tenn cos[21r0'a cos wt] developed in Bessel functions andsinusoidal functions products is devoid in its development of any termwhose argument is in out. The term sin[21'ro'a cos wr] can be written:

sin[21ra-a cos mt]=.l, (21ro'a) cos wt+...

5 in which J l is the Bessel function of order one. Formula (2) cantherefore be written: 1 y' =fB()d TWO-DIMENSIONAL ANALYSIS In this casethere is neither mask nor slit; each column is sequentially scanned atstaggered spatial frequencies and the convolution product:

is made for each object column scanned at the frequency 0', Y denotingthe ordinate on the object and Y denoting the ordinate on the grid whiley, and y denote the ordinates of the ends of the scanned object column(the columns are parallel to the y axis).

As in the first case, the grid is vibrated relatively to the object sothat:

Y'=Y+a coswr Substituting 1" for Y in formula (5) we obtain which can bewritten:

The first term of the second member of formula (7 is constant.

The term at the angular velocity (u is maximum for:

21ra9=l.84

which gives as the previous case the value given by formula (4) for a.The amplitude a cannot be optimized over a wide spatial frequency range;in practice, a ratio ago, of greater than 3 is difficult to obtain.

During an object scan, ais defined for a given object column but eachcolumn is scanned at a different spatial frequency. a must therefore beso determined that the signals at the angular velocity to are maximum onthe average. a is therefore determined from formula (4), the value forbeing taken as:

0-, and 0 having been defined previously.

The invention will now be described in detail with reference to theaccompanying drawings wherein:

FIGS. 1a and lb show the prior art grids used to obtain the odd part andeven part respectively of the Fourier transform of an optical object;

FIG. 2 is a diagrammatic view of a one-dimensional optical objectanalyzer according to the invention;

FIGS. 3a, 3b and 3c are views in greater detail of the same device asshown in FIG. 2 and show inter alia the means for shifting the objectsupport and the grid relatively to the mask and the means for vibratingthe object support relatively to the grid;

FIGS. 4a and 4b show a different one-dimensional analyzer, and

FIG. 5 shows a two-dimensional analyzer.

FIGS. la and lb show the grids which are disclosed in US. Pat. No.3,305,692 and which are used to represent the odd part and even part ofexp (21rjo'y). The grids comprise transparent and opaque parts boundedby equilateral hyperbolae. The equation of the hyperbolae family of thegrid of FIG. 1a is xy=2n D where n denotes a positive or negativeinteger and D denotes a predetermined length. The equation of thehyperbolae family of the grid shown in FIG. lb is xy= (2n-l D Thespatial period l/aalong a straight line of abscissa x is inverselyproportional to the distance x from the straight line in question to theasymptote 0y. Also, the spatial period l/o' along a straight line ofordinate y is inversely proportional to the distance y from the straightline in question to the asymptote 0x. Operation of the analyzer is basedon the proportional relationship between a on the one hand and x and yon the other hand.

Referring to FIG. 2, there can be seen a transparent plate 13 on which atransparent optical object or image 12 has been formed, a mask ll formedwith a slit l0, and a grid 1, the items being placed close together inthe order plate, mask and grid. The grid 1 can be moved uniformly in thedirection perpendicular to the plane of FIG. 2. The plate 13 is vibratedin its plane by an appropriate vibrator 20. The direction of thevibratory movement is unimportant and can be, for instance,-perpendicular to the grid movement direction. A light source 14 disposedat the focal point of a lens 15 projects the optical object or imagethrough grid 1 on to a photoelectric cell or a photomultiplier 16. Theoutput of cell 16 goes to a narrowband filter l9 centered on thevibratory frequency of vibrator 20. The filter I9 is connected to anamplifier 17 which delivers its output to a recorder 18 which recordsfunction (3).

The kind of vibrator used is of no importance for the purposes of thisinvention and should be selected on a basis of frequency and amplitude.For instance, if (r =0.l mm., and 0 0.3 mm., then 0,,==0.2 mm. anda=0.29X0.2 60p..

Referring now to FIGS. 30 to 3c, grid 1 is rigidly secured to astirrup-shaped member 19 having a pin 20 following the threads of ascrew 21 having two'oppositely directed screw threads. Screw 21 ismounted in bearings secured to the mask 11 and is continuously driven bya motor 22 which is also secured to the mask 11. At its ends of travelthe member 19' and the shank of the pin 20 abut abutrnents 23, 24, andthe shank of pin 20 and the abutrnents cooperate to rotate the pin 20around its axis. The pin end in engagement with the threads of screw 21changes its orientation and changes over from the right-hand to theleft-hand screw thread, thus reversing the direction of grid movementrelatively to the mask. Preferably, the pitch of the screw threadcorresponding to the return movement is longer than the screw threadcorresponding to the outward movement.

Mask 11 is formed with an inside recess 25 in which a strip 26 adaptedto mask or unmask slit 10 of mask II can move. The position of strip 26relative to slit 10 is controlled by two levers 27, 28 which are coupledtogether by a rod 29, disposed on mask 11 and articulated relativelythereto and positioned at the two ends of travel of grid 1. The framethereof comprises a rod 30 which cooperates with the bottom parts of thelevers 27, 28 and pivots the same at the end of the outward movement andat the end of the return movement.

Secured to the two ends of lever 27 are the two ends of a piece of pianowire which runs over three deflecting pulleys 32-34 rigidly secured tomask 11 and which is secured to strip 26. As will be readily apparent,when the levers 27, 28 move from the solid line position in FIG. 3b,corresponding to the outward movement of the grid, to the chain-dottedline position, corresponding to the return movement of the grid, strip26 changes from its nonmasking position to its masking position.

At each return of grid 1 (FIG. 30) to its inoperative position itoperates a lever 35 driving an escapement 36 cooperating with a pinion37 which rotates around a spindle secured to mask 11 and which mesheswith a toothed rack 38 rigidly secured to a frame 40. The support 13 ismounted in frame 40 with the interposition of two piezooxide cartridges4], 42 energized in phase opposition by an AC generator (not shown).Frame 40 is biased in one direction by a tension spring 39 secured tothe baseplate of the equipment.

The motion of the parts 1, 11, I3 and 26 is of course the intendedmotion. When motor 22 is switched on the grid reciprocates uniformly butwith an outward movement slower than the return movement. Whenever rod30 operates lever 27, strip 26 masks or closes slit l0. Whenever rod 30operates the levers 27 and 35, strip 26 unmasks or opens slit l0 and,since the escapement operates, the object support 13 is stepped on byone step relative to the mask 11. Also, the support 13 vibratesrelatively to grid 1.

The apparatus shown in FIG. 4a comprises the same elements as theapparatus shown in FIG. 2 except for the vibrator 20 and that theoptical object 12 is not secured to the object support or plate. Theoptical object 43 is projected to form a real image 12 on the support 13which is e.g., a strip of frosted glass. The image 12' is projected by amirror 44 which performs an oscillating motion around an axis which ise.g., perpendicular to slit l0 and parallel to the direction of gridmovement.

On its rear face mirror 44 has (FIG. 4b) two telephonereceiver-typeelectromagnetic devices to vibrate it. More particularly, it has on itsrear face two small soft-iron members 45, 46 acted on by electromagnetseach comprising a silicon iron core 47 and 48 respectively, a soft-ironcylinder 49, 50 respectively and a winding 51, 52 respectively. The twowindings are fed with a direct current and with an alternating currentof the required frequency, the AC coils being oppositely directed ineach of the two windings.

FIG. 5 shows a two-dimensional analyzer comprising an object support 13,which can be of any known kind such as a cathode-ray tube screen or asimple frame for receiving color transparencies or, for instance, afrosted glass screen on which images are formed through a lens. Theoptical object is projected by a lens 15 on the plane of a film 53 andthence via a lens 57 to a photoelectric cell 16. The film 53 forms aclosed loop which runs over rollers 61-64 and which is drivencontinuously by a motor 54 and sprockets 55. A rotating shutter 56 isdriven by the motor 54 and masks the film during changes of view.

The film 53 has been described in detail in US. Pat. No. 3,305,692 andwill not be described again here. All that need be stated is that thefilm represents a number of views of the grid of one of FIGS. la, lb inwhich the y axis is the film-unwinding axis. The grid shifts slightly inthe direction 0x between consecutive views so that any single objectcolumn is scanned at the spatial frequency 0- by one view, at thespatial frequency 0,, ,=a,+Aoby the next and so on.

U.S. Pat. No. 3,305,692 describes different kinds of grids from thoseshown in FIGS. la and 1b. The aim of the invention is of course toobviate the constant component of the Fourier transform or componentsthereof in analyzers of the kind concerned, whatever kind of grid isused, by vibrating the optical object relatively to the grid.

What I claim is:

l. A Fourier transform optical object analyzer comprising a planesupport for an optical object to be analyzed, a mask formed with a slitregistering with a line of the optical object and movable in a planeparallel to the object plane for line-byline unmasking of the object, agrid comprising contiguous transparent and opaque zones bounded bycurves having the same spacing in a first predetermined direction, saidspacing along a line parallel to said first direction varying in inverseproportion to the distance of said line from an origin in a seconddirection of the grid, the first direction being parallel to the maskslit, means for moving step by step the mask relatively to the opticalobject support in said second direction whereby said mask successivelytakes a plurality of discrete positions with regard to said objectsupport, means for continuously moving the grid relatively to the maskin said second direction for each position of the mask, a photosensitivedetector receiving the light flux from the object which has passedthrough the slit and the grid, means for vibrating the grid relative tothe object at a predetermined frequency, and a bandpass filter centeredon such frequency and connected to the output of the photosensitivedetector.

2. A Fourier transform optical object analyzer comprising a planesupport for an optical object to be analyzed, a grid comprisingcontiguous transparent and opaque zones bounded by curves having thesame spacing in a first predetermined direction, said spacing along aline parallel to said first direction varying in inverse proportion tothe distance of said line from an origin in a second direction of thegrid, first means for shifting the grid relatively to the object supportin the second direction whereby the grid takes up a number ofconsecutive discrete positions in which the object support and the gridare offset from one another by multiples of a given pitch, second meansfor continuously shifting the grid relatively to the object support inthe first direction, a photosensitive detector receiving the light fluxfrom the object which has passed through the grid, means for vibratingthe grid relative to the object at a predetermined frequency, and aband-pass filter centered on such frequency and connected to the outputof the photosensitive receiver.

3. An analyzer according to claim 1 wherein the object to be analyzed isprojected on the object support through an optical system oscillating soas to form a vibratory image in the plane of the object support.

4. An analyzer according to claim 2 wherein the object to be analyzed isprojected on the object support through an optical system oscillating soas to form a vibratory image in the plane of the object support.

1. A Fourier transform optical object analyzer comprising a planesupport for an optical object to be analyzed, a mask formed with a slitregistering with a line of the optical object and movable in a planeparallel to the object plane for line-by-line unmasking of the object, agrid comprising contiguous transparent and opaque zones bounded bycurves having the same spacing in a first predetermined direction, saidspacing along a line parallel to said first direction varying in inverseproportion to the distance of said line from an origin in a seconddirection of the grid, the first direction being parallel to the maskslit, means for moving step by step the mask relatively to the opticalobject support in said second direction whereby said mask successivelytakes a plurality of discrete positions with regard to said objectsupport, means for continuously moving the grid relatively to the maskin said second direction for each position of the mask, a photosensitivedetector receiving the light flux from the object which has passedthrough the slit and the grid, means for vibrating the grid relative tothe object at a predetermined frequency, and a band-pass filter centeredon such frequency and connected to the output of the photosensitivedetector.
 2. A Fourier transform optical object analyzer comprising aplane support for an optical object to be analyzed, a grid comprisingcontiguous transparent and opaque zones bounded by curves having thesame spacing in a first predetermined direction, said spacing along aline parallel to said first direction varying in inverse proportion tothe distance of said line from an origin in a second direction of thegrid, first means for shifting the grid relatively to the object supportin the second direction whereby the grid takes up a number ofconsecutive discrete positions in which the object support and the gridare offset from one another by multiples of a given pitch, second meansfor continuously shifting the grid relatively to the object support inthe first direction, a photosensitive detector receiving the light fluxfrom the object which has passed through the grid, means for vibratingthe grid relative to the object at a predetermined frequency, and aband-pass filter centered on such frequency and connected to the outputof the photosensitive receiver.
 3. An analyzer according to claim 1wherein the object to be analyzed is projected on the object supportthrough an optical system oscillating so as to form a vibratory image inthe plane of the object support.
 4. An analyzer according to claim 2wherein the object to be analyzEd is projected on the object supportthrough an optical system oscillating so as to form a vibratory image inthe plane of the object support.